lecture # 15: review for final exam -...

Copyright Copyright ©© by Dr. Hui Hu @ Iowa State University. All Rights Reserved!by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

HHui Huui HuDepartment of Aerospace Engineering, Iowa State University Department of Aerospace Engineering, Iowa State University

Ames, Iowa 50011, U.S.AAmes, Iowa 50011, U.S.A

Lecture # 15: Review for Final ExamLecture # 15: Review for Final Exam

AerEAerE 311L & AerE343L Lecture Notes311L & AerE343L Lecture Notes


AerE343L: AerE343L: Dimensional Analysis and SimilitudeDimensional Analysis and Similitude

Commonly used nonCommonly used non--dimensional parameters:dimensional parameters:

L

force tension surfaceforce inertial WeNumber,Weber

force inertialforce lcentrifugaStr Number, Strohal

forcelity compressibforce inertialM Number,Mach

forcegravity force inertial

lgFr Number, Froude

force viscousforce inertialRe number, Reynolds

force inertialforce pressureEu number,Euler

2

2

∝=

∝=

∝=

∝=

∝=

∝Δ

=

σρ

ϖ

μρ

ρ

lVVl

cV

V

VLVp

Similitude:Similitude:•• Geometric similarity: the model Geometric similarity: the model

have the same shape as the have the same shape as the prototype.prototype.

•• Kinematic similarity: condition Kinematic similarity: condition where the velocity ratio is a where the velocity ratio is a constant between all corresponding constant between all corresponding points in the flow field.points in the flow field.

•• Dynamic similarity: Forces which Dynamic similarity: Forces which act on corresponding masses in the act on corresponding masses in the model flow and prototype flow are model flow and prototype flow are in the same ratio through out the in the same ratio through out the entire flowentire flow


Measurement UncertaintiesMeasurement Uncertainties

•• ““ErrorError”” is the difference between the experimentallyis the difference between the experimentally--determined value and its true value; determined value and its true value; therefore, as error decreases, accuracy is said to increase. therefore, as error decreases, accuracy is said to increase.

•• Total error, Total error, UU, can be considered to be composed of two components:, can be considered to be composed of two components:–– a random (precision) component, a random (precision) component, –– a systematic (bias) component,a systematic (bias) component,–– We usually donWe usually don’’t know these exactly, so we estimate them with t know these exactly, so we estimate them with PP and and BB, respectively., respectively.

222 PBU +=

XTrue valueX=100

Bias errorBias error

precision errorprecision error

measured valueX=101

Both Bias and Precision ErrorsBoth Bias and Precision ErrorsReproducibilityReproducibility

Precision ErrorPrecision ErrorRepeatabilityRepeatability

truemtruemeasurederror AAEAAA −=⇒−=true

errorrelative A

AE =


Measurement UncertaintiesMeasurement Uncertainties

ρρ

ρ

pppV

BernoulliVpp

statictotal

statictotal

Δ=

−=

+=

2)(2

)(,21 2

222RRR PBU +=

Uncertainty in velocity V:Uncertainty in velocity V:

∑∑==

⎥⎦

⎤⎢⎣

⎡∂∂

=⎥⎦

⎤⎢⎣

⎡∂∂

=J

ii

iR

J

ii

iR P

XRPB

XRB

1

22

1

22 ;

∑=

=M

jii j

BB1

2

For a large number of samples (N>10) ii SP 2=

( )[ ] ( ) ⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡−

−= ∑∑

==

N

kkii

N

kikii X

NXXX

NS

1

21

1

2 1;1

1


Pressure Measurement TechniquesPressure Measurement Techniques

•• Deadweight gauges:Deadweight gauges:•• ElasticElastic--element gauges:element gauges:•• Electrical Pressure transducers:Electrical Pressure transducers:•• Wall Pressure measurements Wall Pressure measurements

–– Remote connectionRemote connection–– Cavity mountingCavity mounting–– Flush mountingFlush mounting

•• Pressure Measurements inside Flow FieldPressure Measurements inside Flow Field::


ρ

ρ

)(2

)(,21

0

20

stat

stat

ppV

BernoulliVpp

−=

+=•• Advantage:Advantage:

•• SimpleSimple•• cheapcheap

•• Disadvantage:Disadvantage:•• averaged velocity onlyaveraged velocity only•• Single point measurementsSingle point measurements•• Low measurement accuracyLow measurement accuracy

Velocity measurement techniques Velocity measurement techniques –– PitotPitot ––Static ProbeStatic Probe


Velocity measurement techniques Velocity measurement techniques –– Hotwire ProbeHotwire Probe

•• Advantage:Advantage:•• High accuracyHigh accuracy•• High dynamic responseHigh dynamic response

•• Disadvantage:Disadvantage:•• Single point measurementsSingle point measurements•• Fragile, easy to brokeFragile, easy to broke•• Much more expansive Much more expansive

compared with compared with pitotpitot--static static probe.probe.

Flow Field

Current flow through wire

The rate of which heat is removed from the sensor is directly related to the velocity of the fluid flowing over the sensor

V

•• ConstantConstant--current anemometrycurrent anemometry•• ConstantConstant--temperature anemometrytemperature anemometry

),(2ww

w TVqRidt

dTmc &−=


Particle Image Particle Image VelocimetryVelocimetry (PIV)(PIV)

• To seed fluid flows with small tracer particles (~µm), and assume the tracer particles moving with the same velocity as the low fluid flows.

• To measure the displacements (ΔL) of the tracer particles between known time interval (Δt). The local velocity of fluid flow is calculated by U= Δ L/Δt .

A. t=tA. t=t00 B. t=tB. t=t00+10 +10 μμssClassic 2Classic 2--D PIV measurementD PIV measurement

C. Derived Velocity fieldC. Derived Velocity fieldX (mm)

Y(m

m)

-50 0 50 100 150

-60

-40

-20

0

20

40

60

80

100

-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.95.0 m/sspanwise

vorticity (1/s)

shadow region

GA(W)-1 airfoil

t=tt=t00 tLUΔΔ

=

t= tt= t00++ΔΔttΔΔLL

•• Advantage:Advantage:•• Whole flow field measurementsWhole flow field measurements•• NonNon--intrusive measurementsintrusive measurements

•• Disadvantage:Disadvantage:•• Low temporal resolutionLow temporal resolution•• Very expansive compared with Very expansive compared with

hotwire anemometers and hotwire anemometers and pitotpitot--static probes.static probes.


PIV System SetupPIV System Setup

Illumination system(Laser and optics)

cameraSynchronizer

seed flow withtracer particles

Host computer

Particle tracers: Particle tracers: to track the fluid movement. to track the fluid movement. Illumination system: Illumination system: to illuminate the flow field in the interest region.to illuminate the flow field in the interest region.Camera: Camera: to capture the images of the particle tracers.to capture the images of the particle tracers.Synchronizer: Synchronizer: the control the timing of the laser illumination and the control the timing of the laser illumination and

camera acquisition.camera acquisition.Host computer: Host computer: to store the particle images and conduct image processing. to store the particle images and conduct image processing.


Laminar Flows and Turbulent FlowsLaminar Flows and Turbulent Flows

'';' wwwvvvuuu +=+=+=

...),,,(1 0

0

∫+

=Tt

t

dttzyxuT

u

0'0';0' === wvu

0)'(0)'(;0)'(1)'( 2222

0

>>>= ∫+

wvdtuT

uTt

t

o


Boundary Layer FlowBoundary Layer Flow

yy

∞==

Uu 99.0,yat δ

Displacement thickness:Displacement thickness:

Momentum thickness:Momentum thickness:


AerE343L Lab #1: Pressure Sensor Calibration andAerE343L Lab #1: Pressure Sensor Calibration andMeasurement Uncertainty AnalysisMeasurement Uncertainty Analysis

•• Task #1: Task #1: Pressure Sensor Calibration experimentPressure Sensor Calibration experiment–– A pressure sensor A pressure sensor –– SetraSetra pressure transducer with a range of +/pressure transducer with a range of +/-- 5 inH2O5 inH2O

•• It has two pressure ports: one for total pressure and one for sIt has two pressure ports: one for total pressure and one for static (or reference) pressure.tatic (or reference) pressure.

–– A computer data acquisition system to measure the output voltageA computer data acquisition system to measure the output voltage from the manometer.from the manometer.–– A manometer of known accuracy A manometer of known accuracy

•• MensorMensor Digital Pressure Gage, Model 2101, Range of +/Digital Pressure Gage, Model 2101, Range of +/-- 10 inH2O10 inH2O

–– A plenum and a hand pump to pressurize it. A plenum and a hand pump to pressurize it. –– Tubing to connect pressure sensors and plenumTubing to connect pressure sensors and plenum

•• Lab output:Lab output:–– Calibration curve Calibration curve –– Repeatability of your resultsRepeatability of your results–– Uncertainty of your measurementsUncertainty of your measurements

SetraSetra pressure pressure transducertransducer

(to be calibrated)(to be calibrated)

MensorMensor Digital Digital Pressure GagePressure Gage A computerA computer A plenumA plenum hand pumphand pump

tubingtubing


Lab#02: Lab#02: Airfoil Pressure Distribution Measurements and Calibration of a Small Wind Tunnel

NACA0012 airfoil with 32 pressure tabs

-3.0-2.5-2.0-1.5-1.0-0.5

00.51.01.52.02.53.0

0 1 2 3 4 5 6 7 8 9 10 11 12

X (inches)

Y (i

nche

s)

11

55 10101515

171720202525

3030

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 12 14 16 18 20

CL=2παExperimental data

Angle of Attack (degrees)

Lift

Coe

ffici

ent,

Cl

cV

LCl2

21

∞

=ρ

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 2 4 6 8 10 12 14 16 18 20

Experimental data

Angle of Attack (degrees)

Dra

g C

oeffi

cien

t, C

d

cV

DCd2

21

∞

=ρ


yy

xx80 mm80 mm

Pressure rake with 41 total pressure probesPressure rake with 41 total pressure probes(the distance between the probes d=2mm)(the distance between the probes d=2mm)

Lab 3: Airfoil Wake Measurements and Hotwire Anemometer CalibratLab 3: Airfoil Wake Measurements and Hotwire Anemometer Calibration ion

yy

xx∫

∫

∞∞

∞

∞∞

∞

∞

−=⇒

−==

2

2

22

2

2

)])(1()([221

)])(1()([

21

dyU

yUU

yUC

C

CU

dAU

yUU

yUU

CU

DC

D

D

ρ

ρ

ρ


AerE343L #4: Hot wire measurements in the wake of an airfoilAerE343L #4: Hot wire measurements in the wake of an airfoil

yy

xx

80 mm80 mm

Pressure rake with 41 total pressure probes(the distance between the probes d=2mm)

Hotwire probe

Test conditions: Velocity: V=15 m/sAngle of attack: AOA=0, and 12 deg.Date sampling rate: f=1000HzNumber of samples: 10,000 (10s in time)No. of points: 20~25 pointsGap between points: ~0.2 inches

Lab#3Lab#3

Lab#4Lab#4


AerE343L Lab#5: Measurements of Boundary Layer over a Flat PlatAerE343L Lab#5: Measurements of Boundary Layer over a Flat Platee

XXYY

PitotPitot rakerake

Displacement thickness:Displacement thickness:

Momentum thickness:Momentum thickness:

•• To conduct velocity profile measurements at 10 To conduct velocity profile measurements at 10 downstream locations.downstream locations.

•• To determine boundary layer thickness and drag To determine boundary layer thickness and drag coefficient based on the velocity measurement coefficient based on the velocity measurement results.results.

LCd

θ2=Drag coefficient: Drag coefficient:


AerE343L Lab#6: PIV Measurements of a Flapping WingAerE343L Lab#6: PIV Measurements of a Flapping Wing

X (mm)

Y(m

m)

0 20 40 60

-20

-10

0

10

20

30-1.00 -0.60 -0.20 0.20 0.60 1.00

Spanwise Vorticity(1000*1/s)

X (mm)

Y(m

m)

0 20 40 60

-20

-10

0

10

20

30 -1.20 -0.80 -0.40 0.00 0.40 0.80 1.20

Spanwise Vorticity(1000*1/s)

Flapping frequency: Flapping frequency: f = 60Hzf = 60HzChord length: Chord length: C = 12.7mmC = 12.7mmWing span: Wing span: L = 76.7 mmL = 76.7 mmFlow velocity: Flow velocity: V = 6.36 V = 6.36 m/sm/s

Flapping frequency: Flapping frequency: f = 60Hzf = 60HzChord length: Chord length: C = 12.7mmC = 12.7mmWing span: Wing span: L = 76.7 mmL = 76.7 mmFlow velocity: Flow velocity: V = 1.44 V = 1.44 m/sm/s


AerE311L: The nature of lightAerE311L: The nature of light

•• Light as electromagnetic waves.Light as electromagnetic waves.•• Light as photons.Light as photons.•• Color of lightColor of light•• Index of reflectionIndex of reflection

1/ 0 >==λλvcn

sm /3x10c 80 ≈


Shadowgraph and Shadowgraph and SchlierenSchlieren techniquetechnique

•• Index of refraction:Index of refraction:

•• Depend on variation of index of refraction Depend on variation of index of refraction in a transparent medium and the resulting in a transparent medium and the resulting effect on a light beam passing through the effect on a light beam passing through the test sectiontest section

•• Shadowgraph systems: are used to indicate Shadowgraph systems: are used to indicate the variation of the second derivatives the variation of the second derivatives (normal to the light beam) of the index of (normal to the light beam) of the index of refraction.refraction.

•• SchlierenSchlieren Systems: are used to indicate Systems: are used to indicate the variation of the first derivative of the the variation of the first derivative of the index of refraction index of refraction

1/ 0 >==λλvcn

shadowgraph depicting the flow generated by a bullet shadowgraph depicting the flow generated by a bullet at supersonic speeds. (by Andrew at supersonic speeds. (by Andrew DavidhazyDavidhazy ))

SchlierenSchlieren images of the muzzle blast and images of the muzzle blast and supersonic bullet from firing a .30supersonic bullet from firing a .30--06 caliber 06 caliber highhigh--powered rifle (by Gary S. Settlespowered rifle (by Gary S. Settles ))


Visualization of a Visualization of a SchockwavesSchockwaves using using SchlierenSchlieren techniquetechnique

Before turning on the Supersonic jetBefore turning on the Supersonic jet

After turning on the Supersonic jetAfter turning on the Supersonic jet


Schlieren vs. ShadowgraphSchlieren vs. Shadowgraph

ShadowgraphShadowgraph

•• Displays a mere shadowDisplays a mere shadow•• Shows light ray displacementShows light ray displacement•• Contrast level responds toContrast level responds to

•• No knife edge usedNo knife edge used

SchlierenSchlieren

•• Displays a focused imageDisplays a focused image•• Shows ray refraction angle, Shows ray refraction angle, εε•• Contrast level responds toContrast level responds to

•• Knife edge used for cutoffKnife edge used for cutoffyn∂∂

2

2

yn

∂∂


Review of Quasi-1D Nozzle Flow

uduM

AdA )1( 2 −=

M<1M<1 M>1M>1

Throat Throat M=1M=1

u increasingu increasing

M>1M>1 M<1M<1

Throat Throat M=1M=1

u decreasingu decreasing


1st, 21st, 2ndnd and 3and 3rdrd critic conditionscritic conditions

1st critic 1st critic conditioncondition



P 0 in

crea

sing

P 0 in

crea

sing


AerE311L Lab#1: Visualization of Shockwaves using AerE311L Lab#1: Visualization of Shockwaves using SchlierenSchlierentechniquetechnique

UnderUnder--expanded expanded

flowflow

Flow close to Flow close to 33rdrd criticalcritical

OverOver--expanded expanded

flowflow

22ndnd critical critical –– shock shock is at nozzle exitis at nozzle exit

11stst critical critical –– shock shock is almost at the is almost at the nozzle throat.nozzle throat.


AerE311L Lab#2: Set Up AerE311L Lab#2: Set Up SchlierenSchlieren and Shadowgraph System to and Shadowgraph System to Visualize a Thermal PlumeVisualize a Thermal Plume

Point SourcePoint Source

Candle plumeCandle plume


Tank with compressed airTank with compressed air Test sectionTest section

AerE311L Lab#3: Pressure Measurements in a de Laval NozzleAerE311L Lab#3: Pressure Measurements in a de Laval Nozzle

Tap No. Distance downstream of throat (inches) Area (Sq. inches)1 -4.00 0.8002 -1.50 0.5293 -0.30 0.4804 -0.18 0.4785 0.00 0.4766 0.15 0.4977 0.30 0.5188 0.45 0.5399 0.60 0.56010 0.75 0.58111 0.90 0.59912 1.05 0.61613 1.20 0.62714 1.35 0.63215 1.45 0.634


AerE343L: Final Exam

• Open book• Four problems (25 points each)• ~ 30 minutes


AerE311L: Final Exam

• Open book• 20 multiple-choice problems• ~ 15 minutes

lecture # 15: review for final exam -...

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